def __init__(self, calc, mm, mp, dipoles, finegrid=False): #quadruoles
# Need QM density (on grid) and MM object for CM
self.calc = calc # QM calculator
self.mm = mm # SCME atoms object
self.mp = mp # no. atoms per SCME mol
#
# Interacting with
self.dipoles = dipoles
# self.qpoles = qpoles
#
# LOG
self.timer = Timer()
self.out = sys.stdout
#
self.cm = None
def __init__(self, calculator=None, **kwargs):
self.timer = Timer()
self.set(**kwargs)
if isinstance(calculator, str):
ExcitationList.__init__(self, None, self.txt)
self.filename = calculator
else:
ExcitationList.__init__(self, calculator, self.txt)
if self.filename is not None:
return self.read(self.filename)
if self.eh_comm is None:
self.eh_comm = mpi.serial_comm
elif isinstance(self.eh_comm, (mpi.world.__class__,
mpi.serial_comm.__class__)):
# Correct type already.
pass
else:
# world should be a list of ranks:
self.eh_comm = mpi.world.new_communicator(np.asarray(eh_comm))
if calculator is not None and calculator.initialized:
if calculator.wfs.kpt_comm.size > 1:
err_txt = "Spin parallelization with Linear response "
err_txt += "TDDFT. Use parallel = {'domain' : 'domain_only'} "
err_txt += "calculator parameter."
raise NotImplementedError(err_txt)
if self.xc == 'GS':
self.xc = calculator.hamiltonian.xc.name
calculator.converge_wave_functions()
if calculator.density.nct_G is None:
spos_ac = calculator.initialize_positions()
calculator.wfs.initialize(calculator.density,
calculator.hamiltonian, spos_ac)
self.update(calculator)
def __init__(self, mm, qm, mp, calcmm, dyn=False, g=0.5):
self.mm = mm # mm atoms object
self.mp = mp # no. atoms per center of mass (cm)
self.dyn = dyn # dyn. update of potential?
self.calcmm = calcmm # mm calculator (SCME)
self.qm = qm # qm atoms object
#
self.qmidx = len(qm)# no. QM atoms
#
self.nm = len(self.mm) / self.mp
self.cm = self.get_cm(self.nm)
self.timer = Timer()
# smoothing value
self.g = g
# initialization
self.initial = True
# Hold on to old arrays
self.dipoles = None
self.qpoles = None
self.dipoles_1 = None
self.qpoles_1 = None
class LrTDDFT(ExcitationList):
"""Linear Response TDDFT excitation class
Input parameters:
calculator:
the calculator object after a ground state calculation
nspins:
number of spins considered in the calculation
Note: Valid only for unpolarised ground state calculation
eps:
Minimal occupation difference for a transition (default 0.001)
istart:
First occupied state to consider
jend:
Last unoccupied state to consider
xc:
Exchange-Correlation approximation in the Kernel
derivative_level:
0: use Exc, 1: use vxc, 2: use fxc if available
filename:
read from a file
"""
def __init__(self, calculator=None, **kwargs):
self.timer = Timer()
self.set(**kwargs)
if isinstance(calculator, str):
ExcitationList.__init__(self, None, self.txt)
self.filename = calculator
else:
ExcitationList.__init__(self, calculator, self.txt)
if self.filename is not None:
return self.read(self.filename)
if self.eh_comm is None:
self.eh_comm = mpi.serial_comm
elif isinstance(self.eh_comm, (mpi.world.__class__,
mpi.serial_comm.__class__)):
# Correct type already.
pass
else:
# world should be a list of ranks:
self.eh_comm = mpi.world.new_communicator(np.asarray(eh_comm))
if calculator is not None and calculator.initialized:
if calculator.wfs.kpt_comm.size > 1:
err_txt = "Spin parallelization with Linear response "
err_txt += "TDDFT. Use parallel = {'domain' : 'domain_only'} "
err_txt += "calculator parameter."
raise NotImplementedError(err_txt)
if self.xc == 'GS':
self.xc = calculator.hamiltonian.xc.name
calculator.converge_wave_functions()
if calculator.density.nct_G is None:
spos_ac = calculator.initialize_positions()
calculator.wfs.initialize(calculator.density,
calculator.hamiltonian, spos_ac)
self.update(calculator)
def set(self, **kwargs):
defaults = {
'nspins' : None,
'eps' : 0.001,
'istart' : 0,
'jend' : None,
'energy_range' : None,
'xc' : 'GS',
'derivative_level' : 1,
'numscale' : 0.00001,
'txt' : None,
'filename' : None,
'finegrid' : 2,
'force_ApmB' : False, # for tests
'eh_comm' : None # parallelization over eh-pairs
}
changed = False
for key, value in defaults.items():
if hasattr(self, key):
value = getattr(self, key) # do not overwrite
setattr(self, key, kwargs.pop(key, value))
if value != getattr(self, key):
changed = True
for key in kwargs:
raise KeyError('Unknown key ' + key)
return changed
def set_calculator(self, calculator):
self.calculator = calculator
# self.force_ApmB = parameters['force_ApmB']
self.force_ApmB = None # XXX
def analyse(self, what=None, out=None, min=0.1):
"""Print info about the transitions.
Parameters:
1. what: I list of excitation indicees, None means all
2. out : I where to send the output, None means sys.stdout
3. min : I minimal contribution to list (0<min<1)
"""
if what is None:
what = range(len(self))
elif isinstance(what, int):
what = [what]
if out is None:
out = sys.stdout
for i in what:
print >> out, str(i) + ':', self[i].analyse(min=min)
def update(self, calculator=None, **kwargs):
changed = self.set(**kwargs)
if calculator is not None:
changed = True
self.set_calculator(calculator)
if not changed:
return
self.forced_update()
def forced_update(self):
"""Recalc yourself."""
nonselfconsistent_xc = None
if not self.force_ApmB:
Om = OmegaMatrix
name = 'LrTDDFT'
if self.xc:
xc = XC(self.xc)
if hasattr(xc, 'hybrid') and xc.hybrid > 0.0:
Om = ApmB
name = 'LrTDDFThyb'
# nonselfconsistent_xc = HybridXC('PBE0', alpha=5.0)
else:
Om = ApmB
name = 'LrTDDFThyb'
self.kss = KSSingles(calculator=self.calculator,
nspins=self.nspins,
nonselfconsistent_xc=nonselfconsistent_xc,
eps=self.eps,
istart=self.istart,
jend=self.jend,
energy_range=self.energy_range,
txt=self.txt)
self.Om = Om(self.calculator, self.kss,
self.xc, self.derivative_level, self.numscale,
finegrid=self.finegrid, eh_comm=self.eh_comm,
txt=self.txt)
self.name = name
def diagonalize(self, istart=None, jend=None,
energy_range=None, TDA=False):
self.timer.start('diagonalize')
self.timer.start('omega')
self.Om.diagonalize(istart, jend, energy_range, TDA)
self.timer.stop('omega')
# remove old stuff
self.timer.start('clean')
while len(self): self.pop()
self.timer.stop('clean')
print >> self.txt, 'LrTDDFT digonalized:'
self.timer.start('build')
for j in range(len(self.Om.kss)):
self.append(LrTDDFTExcitation(self.Om, j))
print >> self.txt, ' ', str(self[-1])
self.timer.stop('build')
self.timer.stop('diagonalize')
def get_Om(self):
return self.Om
def read(self, filename=None, fh=None):
"""Read myself from a file"""
if fh is None:
if filename.endswith('.gz'):
try:
import gzip
f = gzip.open(filename)
except:
f = open(filename, 'r')
else:
f = open(filename, 'r')
self.filename = filename
else:
f = fh
self.filename = None
# get my name
s = f.readline().replace('\n','')
self.name = s.split()[1]
self.xc = f.readline().replace('\n','').split()[0]
values = f.readline().split()
self.eps = float(values[0])
if len(values) > 1:
self.derivative_level = int(values[1])
self.numscale = float(values[2])
self.finegrid = int(values[3])
else:
# old writing style, use old defaults
self.numscale = 0.001
self.kss = KSSingles(filehandle=f)
if self.name == 'LrTDDFT':
self.Om = OmegaMatrix(kss=self.kss, filehandle=f,
txt=self.txt)
else:
self.Om = ApmB(kss=self.kss, filehandle=f,
txt=self.txt)
self.Om.Kss(self.kss)
# check if already diagonalized
p = f.tell()
s = f.readline()
if s != '# Eigenvalues\n':
# go back to previous position
f.seek(p)
else:
# load the eigenvalues
n = int(f.readline().split()[0])
for i in range(n):
self.append(LrTDDFTExcitation(string=f.readline()))
# load the eigenvectors
f.readline()
for i in range(n):
values = f.readline().split()
weights = [float(val) for val in values]
self[i].f = np.array(weights)
self[i].kss = self.kss
if fh is None:
f.close()
# update own variables
self.istart = self.Om.fullkss.istart
self.jend = self.Om.fullkss.jend
def singlets_triplets(self):
"""Split yourself into a singlet and triplet object"""
slr = LrTDDFT(None, nspins=self.nspins, eps=self.eps,
istart=self.istart, jend=self.jend, xc=self.xc,
derivative_level=self.derivative_level,
numscale=self.numscale)
tlr = LrTDDFT(None, nspins=self.nspins, eps=self.eps,
istart=self.istart, jend=self.jend, xc=self.xc,
derivative_level=self.derivative_level,
numscale=self.numscale)
slr.Om, tlr.Om = self.Om.singlets_triplets()
for lr in [slr, tlr]:
lr.kss = lr.Om.fullkss
return slr, tlr
def single_pole_approximation(self, i, j):
"""Return the excitation according to the
single pole approximation. See e.g.:
Grabo et al, Theochem 501 (2000) 353-367
"""
for ij, kss in enumerate(self.kss):
if kss.i == i and kss.j == j:
return sqrt(self.Om.full[ij][ij]) * Hartree
return self.Om.full[ij][ij] / kss.energy * Hartree
def __str__(self):
string = ExcitationList.__str__(self)
string += '# derived from:\n'
string += self.Om.kss.__str__()
return string
def write(self, filename=None, fh=None):
"""Write current state to a file.
'filename' is the filename. If the filename ends in .gz,
the file is automatically saved in compressed gzip format.
'fh' is a filehandle. This can be used to write into already
opened files.
"""
if mpi.rank == mpi.MASTER:
if fh is None:
if filename.endswith('.gz'):
try:
import gzip
f = gzip.open(filename,'wb')
except:
f = open(filename, 'w')
else:
f = open(filename, 'w')
else:
f = fh
f.write('# ' + self.name + '\n')
xc = self.xc
if xc is None: xc = 'RPA'
if self.calculator is not None:
xc += ' ' + self.calculator.get_xc_functional()
f.write(xc + '\n')
f.write('%g %d %g %d' % (self.eps, int(self.derivative_level),
self.numscale, int(self.finegrid)) + '\n')
self.kss.write(fh=f)
self.Om.write(fh=f)
if len(self):
f.write('# Eigenvalues\n')
istart = self.istart
if istart is None:
istart = self.kss.istart
jend = self.jend
if jend is None:
jend = self.kss.jend
f.write('%d %d %d'%(len(self), istart, jend) + '\n')
for ex in self:
f.write(ex.outstring())
f.write('# Eigenvectors\n')
for ex in self:
for w in ex.f:
f.write('%g '%w)
f.write('\n')
if fh is None:
f.close()
class DipoleDensityForces:
def __init__(self, calc, mm, mp, dipoles, finegrid=False): #quadruoles
# Need QM density (on grid) and MM object for CM
self.calc = calc # QM calculator
self.mm = mm # SCME atoms object
self.mp = mp # no. atoms per SCME mol
#
# Interacting with
self.dipoles = dipoles
# self.qpoles = qpoles
#
# LOG
self.timer = Timer()
self.out = sys.stdout
#
self.cm = None
def calculate_forces(self):
self.out.write('Calculating E-dens to MM Forces')
self.timer.start('E-dens to MM Forces')
#
if self.cm is None:
self.get_cm()
# Force array
n = len(self.atoms) / self.mp
F = np.zeros((3,n))
#
calc = self.calc
# Grab grid descriptor and density
if self.finegd:
gd = calc.density.finegd
# Get dens on fg
if calc.density.nt_sg is None:
calc.density.interpolate_pseudo_density()
nt_sg = calc.density.nt_sg
#
else:
gd = calc.density.gd
nt_sg = calc.density.nt_sG
#
if calc.density.nspins == 1:
nt_g = nt_sg[0]
else:
nt_g = nt_sg.sum(axis=1)
#
sg = (np.indices(gd.n_c, float).T + \
gd.beg_c) / gd.N_c
#
for a, pos in enumerate(self.cm):
# Get all scaled gpt distance to cm
asg = sg - np.linalg.solve(gd.cell_cv.T, pos)
# r(xyz) - in Ang
xyz = np.dot(asg, gd.cell_cv) * Bohr
#
dis = np.sqrt(((xyz.T)**2).sum(axis=0))
# n(r)/d**3
n_d = nt_sg / dis**3
# p*r
pr_r = xyz.T*np.dot(xyz, self.dipole[a])
# whole term (with electrostatic constant)
tot = k_c * n_d * (self.dipole[a] - 3*pr_r.T).T
#
# new = tot.reshape((3,tot[1]*tot[2]*tot[3] in shape))
#
F[:,a] = [tot[0].sum(), tot[1].sum(), tot[2].sum()]
self.timer.stop('E-dens to MM Forces')
self.out.write(' E-dens/MM Forces took: %.3f sec'
%self.timer.timers[('E-dens to MM Forces',)])
return F
def get_cm(self):
""" Get CM for SCME mols in units [Bohr]
"""
#
atoms = self.mm
mp = self.mp
n = len(self.atoms) / self.mp
cm = np.zeros((n,3))
#
for i in range(n):
cm[i,:] += atoms[i*mp:(i+1)*mp].get_center_of_mass() / Bohr
#
self.cm = cm.copy()
def test_inv_speed(self):
full_mat = self.recover()
timer = Timer()
timer.start('full_numpy')
tmp0 = np.linalg.inv(full_mat)
timer.stop('full_numpy')
timer.start('full_lapack')
inverse_general(full_mat)
timer.stop('full_lapack')
timer.start('sparse_lapack')
self.inv_eq()
timer.stop('sparse_lapack')
timer.start('sparse_lapack_ne')
self.inv_ne()
timer.stop('sparse_lapack_ne')
times = []
methods = ['full_numpy', 'full_lapack', 'sparse_lapack']
for name in methods:
time = timer.timers[name,]
print name, time
times.append(time)
mintime = np.min(times)
self.inv_method = methods[np.argmin(times)]
print 'mintime', mintime
print 'sparse_lapack_ne', timer.timers['sparse_lapack_ne',]
import sys
from ase import Atoms, Atom
from gpaw import GPAW
from gpaw.test import equal
from gpaw.utilities.timing import Timer
from gpaw.xc.hybrid import HybridXC
timer = Timer()
loa = Atoms('Be2',
[(0, 0, 0), (2.45, 0, 0)],
magmoms=[0.5, 0.5],
cell=[5.9, 4.8, 5.0])
loa.center()
fgl = [False, True]
#fgl = [True, False]
txt='-'
txt='/dev/null'
E = {}
niter = {}
for fg in fgl:
if fg:
tstr = 'Exx on fine grid'
else:
tstr = 'Exx on coarse grid'
timer.start(tstr)
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss=self.fullkss
finegrid=self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print >> self.txt,'RPA',nij,'transitions'
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'RPA kss['+'%d'%ij+']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
## print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p,phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij,nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = 2 * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight() )
I = self.Coulomb_integral_kss(kss[ij], kss[kq],
rhot, phit, timer2)
Om[ij,kq] = pre * I
if ij == kq:
Om[ij,kq] += kss[ij].get_energy()**2
else:
Om[kq,ij]=Om[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5*t*(nij-ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPA estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins==2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins==2:
# construct spin polarised densities
nt_sg = np.array([.5*paw.density.nt_sg[0],
.5*paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel==0:
raise NotImplementedError
if kss.npspins==2:
v_g=nt_sg[0].copy()
else:
v_g=nt_sg.copy()
elif self.derivativeLevel==1:
pass
elif self.derivativeLevel==2:
fxc_sg = np.zeros(nt_sg.shape)
self.xc.calculate_fxc(gd, nt_sg, fxc_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
## self.paw.my_nuclei = []
ns=self.numscale
xc=self.xc
print >> self.txt, 'XC',nij,'transitions'
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'XC kss['+'%d'%ij+']'
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel >= 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s=np.zeros(nt_s.shape,nt_s.dtype.char)
vm_s=np.zeros(nt_s.shape,nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
self.xc.calculate_paw_correction(setup, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij,nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins==2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] += kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(
nv_g[0], v_g, nv_g[1], v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] += kss[ij].get(fg)
nv_g[kss[kq].pspin] -= kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
else: # spin unpolarised
nv_g=nt_sg + ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg + ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g,v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g,v_g)
Om_xc[ij,kq] += weight *\
0.25*(Excpp-Excmp-Excpm+Excmm)/(ns*ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij,kq] += weight*\
self.gd.integrate(kss[kq].get(fg)*
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins==2: # spin polarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg[kss[ij].pspin, kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg) *
kss[kq].get(fg) *
fxc_sg)
# XXX still numeric derivatives for local terms
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
if ij != kq:
Om_xc[kq,ij] = Om_xc[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
print >> self.txt,'XC estimated time left',\
self.time_left(timer, t0, ij, nij)
def __init__(self, name, hybrid=None, xc=None,
alpha=None,
gamma_point=1,
method='standard',
bandstructure=False,
logfilename='-', bands=None,
fcut=1e-10,
molecule=False,
qstride=1,
world=None):
"""Mix standard functionals with exact exchange.
name: str
Name of functional: EXX, PBE0, HSE03, HSE06
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
method: str
Use 'standard' standard formula and 'acdf for
adiabatic-connection dissipation fluctuation formula.
alpha: float
XXX describe
gamma_point: bool
0: Skip k2-k1=0 interactions.
1: Use the alpha method.
2: Integrate the gamma point.
bandstructure: bool
Calculate bandstructure instead of just the total energy.
bands: list of int
List of bands to calculate bandstructure for. Default is
all bands.
molecule: bool
Decouple electrostatic interactions between periodically
repeated images.
fcut: float
Threshold for empty band.
"""
self.alpha = alpha
self.fcut = fcut
self.gamma_point = gamma_point
self.method = method
self.bandstructure = bandstructure
self.bands = bands
self.fd = logfilename
self.write_timing_information = True
HybridXCBase.__init__(self, name, hybrid, xc)
# EXX energies:
self.exx = None # total
self.evv = None # valence-valence (pseudo part)
self.evvacdf = None # valence-valence (pseudo part)
self.devv = None # valence-valence (PAW correction)
self.evc = None # valence-core
self.ecc = None # core-core
self.exx_skn = None # bandstructure
self.qlatest = None
if world is None:
world = mpi.world
self.world = world
self.molecule = molecule
if isinstance(qstride, int):
qstride = [qstride] * 3
self.qstride_c = np.asarray(qstride)
self.timer = Timer()
class HybridXC(HybridXCBase):
orbital_dependent = True
def __init__(self, name, hybrid=None, xc=None,
alpha=None,
gamma_point=1,
method='standard',
bandstructure=False,
logfilename='-', bands=None,
fcut=1e-10,
molecule=False,
qstride=1,
world=None):
"""Mix standard functionals with exact exchange.
name: str
Name of functional: EXX, PBE0, HSE03, HSE06
hybrid: float
Fraction of exact exchange.
xc: str or XCFunctional object
Standard DFT functional with scaled down exchange.
method: str
Use 'standard' standard formula and 'acdf for
adiabatic-connection dissipation fluctuation formula.
alpha: float
XXX describe
gamma_point: bool
0: Skip k2-k1=0 interactions.
1: Use the alpha method.
2: Integrate the gamma point.
bandstructure: bool
Calculate bandstructure instead of just the total energy.
bands: list of int
List of bands to calculate bandstructure for. Default is
all bands.
molecule: bool
Decouple electrostatic interactions between periodically
repeated images.
fcut: float
Threshold for empty band.
"""
self.alpha = alpha
self.fcut = fcut
self.gamma_point = gamma_point
self.method = method
self.bandstructure = bandstructure
self.bands = bands
self.fd = logfilename
self.write_timing_information = True
HybridXCBase.__init__(self, name, hybrid, xc)
# EXX energies:
self.exx = None # total
self.evv = None # valence-valence (pseudo part)
self.evvacdf = None # valence-valence (pseudo part)
self.devv = None # valence-valence (PAW correction)
self.evc = None # valence-core
self.ecc = None # core-core
self.exx_skn = None # bandstructure
self.qlatest = None
if world is None:
world = mpi.world
self.world = world
self.molecule = molecule
if isinstance(qstride, int):
qstride = [qstride] * 3
self.qstride_c = np.asarray(qstride)
self.timer = Timer()
def log(self, *args, **kwargs):
prnt(file=self.fd, *args, **kwargs)
self.fd.flush()
def calculate_radial(self, rgd, n_sLg, Y_L, v_sg,
dndr_sLg=None, rnablaY_Lv=None,
tau_sg=None, dedtau_sg=None):
return self.xc.calculate_radial(rgd, n_sLg, Y_L, v_sg,
dndr_sLg, rnablaY_Lv)
def calculate_paw_correction(self, setup, D_sp, dEdD_sp=None,
addcoredensity=True, a=None):
return self.xc.calculate_paw_correction(setup, D_sp, dEdD_sp,
addcoredensity, a)
def initialize(self, dens, ham, wfs, occupations):
assert wfs.bd.comm.size == 1
self.xc.initialize(dens, ham, wfs, occupations)
self.dens = dens
self.wfs = wfs
# Make a k-point descriptor that is not distributed
# (self.kd.comm is serial_comm):
self.kd = wfs.kd.copy()
self.fd = logfile(self.fd, self.world.rank)
wfs.initialize_wave_functions_from_restart_file()
def set_positions(self, spos_ac):
self.spos_ac = spos_ac
def calculate(self, gd, n_sg, v_sg=None, e_g=None):
# Normal XC contribution:
exc = self.xc.calculate(gd, n_sg, v_sg, e_g)
# Add EXX contribution:
return exc + self.exx * self.hybrid
def calculate_exx(self):
"""Non-selfconsistent calculation."""
self.timer.start('EXX')
self.timer.start('Initialization')
kd = self.kd
wfs = self.wfs
if fftw.FFTPlan is fftw.NumpyFFTPlan:
self.log('NOT USING FFTW !!')
self.log('Spins:', self.wfs.nspins)
W = max(1, self.wfs.kd.comm.size // self.wfs.nspins)
# Are the k-points distributed?
kparallel = (W > 1)
# Find number of occupied bands:
self.nocc_sk = np.zeros((self.wfs.nspins, kd.nibzkpts), int)
for kpt in self.wfs.kpt_u:
for n, f in enumerate(kpt.f_n):
if abs(f) < self.fcut:
self.nocc_sk[kpt.s, kpt.k] = n
break
else:
self.nocc_sk[kpt.s, kpt.k] = self.wfs.bd.nbands
self.wfs.kd.comm.sum(self.nocc_sk)
noccmin = self.nocc_sk.min()
noccmax = self.nocc_sk.max()
self.log('Number of occupied bands (min, max): %d, %d' %
(noccmin, noccmax))
self.log('Number of valence electrons:', self.wfs.setups.nvalence)
if self.bandstructure:
self.log('Calculating eigenvalue shifts.')
# allocate array for eigenvalue shifts:
self.exx_skn = np.zeros((self.wfs.nspins,
kd.nibzkpts,
self.wfs.bd.nbands))
if self.bands is None:
noccmax = self.wfs.bd.nbands
else:
noccmax = max(max(self.bands) + 1, noccmax)
N_c = self.kd.N_c
vol = wfs.gd.dv * wfs.gd.N_c.prod()
if self.alpha is None:
alpha = 6 * vol**(2 / 3.0) / pi**2
else:
alpha = self.alpha
if self.gamma_point == 1:
if alpha == 0.0:
qvol = (2*np.pi)**3 / vol / N_c.prod()
self.gamma = 4*np.pi * (3*qvol / (4*np.pi))**(1/3.) / qvol
else:
self.gamma = self.calculate_gamma(vol, alpha)
else:
kcell_cv = wfs.gd.cell_cv.copy()
kcell_cv[0] *= N_c[0]
kcell_cv[1] *= N_c[1]
kcell_cv[2] *= N_c[2]
self.gamma = madelung(kcell_cv) * vol * N_c.prod() / (4 * np.pi)
self.log('Value of alpha parameter: %.3f Bohr^2' % alpha)
self.log('Value of gamma parameter: %.3f Bohr^2' % self.gamma)
# Construct all possible q=k2-k1 vectors:
Nq_c = (N_c - 1) // self.qstride_c
i_qc = np.indices(Nq_c * 2 + 1, float).transpose(
(1, 2, 3, 0)).reshape((-1, 3))
self.bzq_qc = (i_qc - Nq_c) / N_c * self.qstride_c
self.q0 = ((Nq_c * 2 + 1).prod() - 1) // 2 # index of q=(0,0,0)
assert not self.bzq_qc[self.q0].any()
# Count number of pairs for each q-vector:
self.npairs_q = np.zeros(len(self.bzq_qc), int)
for s in range(kd.nspins):
for k1 in range(kd.nibzkpts):
for k2 in range(kd.nibzkpts):
for K2, q, n1_n, n2 in self.indices(s, k1, k2):
self.npairs_q[q] += len(n1_n)
self.npairs0 = self.npairs_q.sum() # total number of pairs
self.log('Number of pairs:', self.npairs0)
# Distribute q-vectors to Q processors:
Q = self.world.size // self.wfs.kd.comm.size
myrank = self.world.rank // self.wfs.kd.comm.size
rank = 0
N = 0
myq = []
nq = 0
for q, n in enumerate(self.npairs_q):
if n > 0:
nq += 1
if rank == myrank:
myq.append(q)
N += n
if N >= (rank + 1.0) * self.npairs0 / Q:
rank += 1
assert len(myq) > 0, 'Too few q-vectors for too many processes!'
self.bzq_qc = self.bzq_qc[myq]
try:
self.q0 = myq.index(self.q0)
except ValueError:
self.q0 = None
self.log('%d x %d x %d k-points' % tuple(self.kd.N_c))
self.log('Distributing %d IBZ k-points over %d process(es).' %
(kd.nibzkpts, self.wfs.kd.comm.size))
self.log('Distributing %d q-vectors over %d process(es).' % (nq, Q))
# q-point descriptor for my q-vectors:
qd = KPointDescriptor(self.bzq_qc)
# Plane-wave descriptor for all wave-functions:
self.pd = PWDescriptor(wfs.pd.ecut, wfs.gd,
dtype=wfs.pd.dtype, kd=kd)
# Plane-wave descriptor pair-densities:
self.pd2 = PWDescriptor(self.dens.pd2.ecut, self.dens.gd,
dtype=wfs.dtype, kd=qd)
self.log('Cutoff energies:')
self.log(' Wave functions: %10.3f eV' %
(self.pd.ecut * Hartree))
self.log(' Density: %10.3f eV' %
(self.pd2.ecut * Hartree))
# Calculate 1/|G+q|^2 with special treatment of |G+q|=0:
G2_qG = self.pd2.G2_qG
if self.q0 is None:
if self.omega is None:
self.iG2_qG = [1.0 / G2_G for G2_G in G2_qG]
else:
self.iG2_qG = [(1.0 / G2_G *
(1 - np.exp(-G2_G / (4 * self.omega**2))))
for G2_G in G2_qG]
else:
G2_qG[self.q0][0] = 117.0 # avoid division by zero
if self.omega is None:
self.iG2_qG = [1.0 / G2_G for G2_G in G2_qG]
self.iG2_qG[self.q0][0] = self.gamma
else:
self.iG2_qG = [(1.0 / G2_G *
(1 - np.exp(-G2_G / (4 * self.omega**2))))
for G2_G in G2_qG]
self.iG2_qG[self.q0][0] = 1 / (4 * self.omega**2)
G2_qG[self.q0][0] = 0.0 # restore correct value
# Compensation charges:
self.ghat = PWLFC([setup.ghat_l for setup in wfs.setups], self.pd2)
self.ghat.set_positions(self.spos_ac)
if self.molecule:
self.initialize_gaussian()
self.log('Value of beta parameter: %.3f 1/Bohr^2' % self.beta)
self.timer.stop('Initialization')
# Ready ... set ... go:
self.t0 = time()
self.npairs = 0
self.evv = 0.0
self.evvacdf = 0.0
for s in range(self.wfs.nspins):
kpt1_q = [KPoint(self.wfs, noccmax).initialize(kpt)
for kpt in self.wfs.kpt_u if kpt.s == s]
kpt2_q = kpt1_q[:]
if len(kpt1_q) == 0:
# No s-spins on this CPU:
continue
# Send and receive ranks:
srank = self.wfs.kd.get_rank_and_index(
s, (kpt1_q[0].k - 1) % kd.nibzkpts)[0]
rrank = self.wfs.kd.get_rank_and_index(
s, (kpt1_q[-1].k + 1) % kd.nibzkpts)[0]
# Shift k-points kd.nibzkpts - 1 times:
for i in range(kd.nibzkpts):
if i < kd.nibzkpts - 1:
if kparallel:
kpt = kpt2_q[-1].next(self.wfs)
kpt.start_receiving(rrank)
kpt2_q[0].start_sending(srank)
else:
kpt = kpt2_q[0]
self.timer.start('Calculate')
for kpt1, kpt2 in zip(kpt1_q, kpt2_q):
# Loop over all k-points that k2 can be mapped to:
for K2, q, n1_n, n2 in self.indices(s, kpt1.k, kpt2.k):
self.apply(K2, q, kpt1, kpt2, n1_n, n2)
self.timer.stop('Calculate')
if i < kd.nibzkpts - 1:
self.timer.start('Wait')
if kparallel:
kpt.wait()
kpt2_q[0].wait()
self.timer.stop('Wait')
kpt2_q.pop(0)
kpt2_q.append(kpt)
self.evv = self.world.sum(self.evv)
self.evvacdf = self.world.sum(self.evvacdf)
self.calculate_exx_paw_correction()
if self.method == 'standard':
self.exx = self.evv + self.devv + self.evc + self.ecc
elif self.method == 'acdf':
self.exx = self.evvacdf + self.devv + self.evc + self.ecc
else:
1 / 0
self.log('Exact exchange energy:')
for txt, e in [
('core-core', self.ecc),
('valence-core', self.evc),
('valence-valence (pseudo, acdf)', self.evvacdf),
('valence-valence (pseudo, standard)', self.evv),
('valence-valence (correction)', self.devv),
('total (%s)' % self.method, self.exx)]:
self.log(' %-36s %14.6f eV' % (txt + ':', e * Hartree))
self.log('Total time: %10.3f seconds' % (time() - self.t0))
self.npairs = self.world.sum(self.npairs)
assert self.npairs == self.npairs0
self.timer.stop('EXX')
self.timer.write(self.fd)
def calculate_gamma(self, vol, alpha):
if self.molecule:
return 0.0
N_c = self.kd.N_c
offset_c = (N_c + 1) % 2 * 0.5 / N_c
bzq_qc = monkhorst_pack(N_c) + offset_c
qd = KPointDescriptor(bzq_qc)
pd = PWDescriptor(self.wfs.pd.ecut, self.wfs.gd, kd=qd)
gamma = (vol / (2 * pi)**2 * sqrt(pi / alpha) *
self.kd.nbzkpts)
for G2_G in pd.G2_qG:
if G2_G[0] < 1e-7:
G2_G = G2_G[1:]
gamma -= np.dot(np.exp(-alpha * G2_G), G2_G**-1)
return gamma / self.qstride_c.prod()
def indices(self, s, k1, k2):
"""Generator for (K2, q, n1, n2) indices for (k1, k2) pair.
s: int
Spin index.
k1: int
Index of k-point in the IBZ.
k2: int
Index of k-point in the IBZ.
Returns (K, q, n1_n, n2), where K then index of the k-point in
the BZ that k2 is mapped to, q is the index of the q-vector
between K and k1, and n1_n is a list of bands that should be
combined with band n2."""
for K, k in enumerate(self.kd.bz2ibz_k):
if k == k2:
for K, q, n1_n, n2 in self._indices(s, k1, k2, K):
yield K, q, n1_n, n2
def _indices(self, s, k1, k2, K2):
k1_c = self.kd.ibzk_kc[k1]
k2_c = self.kd.bzk_kc[K2]
q_c = k2_c - k1_c
q = abs(self.bzq_qc - q_c).sum(1).argmin()
if abs(self.bzq_qc[q] - q_c).sum() > 1e-7:
return
if self.gamma_point == 0 and q == self.q0:
return
nocc1 = self.nocc_sk[s, k1]
nocc2 = self.nocc_sk[s, k2]
# Is k2 in the IBZ?
is_ibz2 = (self.kd.ibz2bz_k[k2] == K2)
for n2 in range(self.wfs.bd.nbands):
# Find range of n1's (from n1a to n1b-1):
if is_ibz2:
# We get this combination twice, so let's only do half:
if k1 >= k2:
n1a = n2
else:
n1a = n2 + 1
else:
n1a = 0
n1b = self.wfs.bd.nbands
if self.bandstructure:
if n2 >= nocc2:
n1b = min(n1b, nocc1)
else:
if n2 >= nocc2:
break
n1b = min(n1b, nocc1)
if self.bands is not None:
assert self.bandstructure
n1_n = []
for n1 in range(n1a, n1b):
if (n1 in self.bands and n2 < nocc2 or
is_ibz2 and n2 in self.bands and n1 < nocc1):
n1_n.append(n1)
n1_n = np.array(n1_n)
else:
n1_n = np.arange(n1a, n1b)
if len(n1_n) == 0:
continue
yield K2, q, n1_n, n2
def apply(self, K2, q, kpt1, kpt2, n1_n, n2):
k20_c = self.kd.ibzk_kc[kpt2.k]
k2_c = self.kd.bzk_kc[K2]
if k2_c.any():
self.timer.start('Initialize plane waves')
eik2r_R = self.wfs.gd.plane_wave(k2_c)
eik20r_R = self.wfs.gd.plane_wave(k20_c)
self.timer.stop('Initialize plane waves')
else:
eik2r_R = 1.0
eik20r_R = 1.0
w1 = self.kd.weight_k[kpt1.k]
w2 = self.kd.weight_k[kpt2.k]
# Is k2 in the 1. BZ?
is_ibz2 = (self.kd.ibz2bz_k[kpt2.k] == K2)
e_n = self.calculate_interaction(n1_n, n2, kpt1, kpt2, q, K2,
eik20r_R, eik2r_R,
is_ibz2)
e_n *= 1.0 / self.kd.nbzkpts / self.wfs.nspins * self.qstride_c.prod()
if q == self.q0:
e_n[n1_n == n2] *= 0.5
f1_n = kpt1.f_n[n1_n]
eps1_n = kpt1.eps_n[n1_n]
f2 = kpt2.f_n[n2]
eps2 = kpt2.eps_n[n2]
s_n = np.sign(eps2 - eps1_n)
evv = (f1_n * f2 * e_n).sum()
evvacdf = 0.5 * (f1_n * (1 - s_n) * e_n +
f2 * (1 + s_n) * e_n).sum()
self.evv += evv * w1
self.evvacdf += evvacdf * w1
if is_ibz2:
self.evv += evv * w2
self.evvacdf += evvacdf * w2
if self.bandstructure:
x = self.wfs.nspins
self.exx_skn[kpt1.s, kpt1.k, n1_n] += x * f2 * e_n
if is_ibz2:
self.exx_skn[kpt2.s, kpt2.k, n2] += x * np.dot(f1_n, e_n)
def calculate_interaction(self, n1_n, n2, kpt1, kpt2, q, k,
eik20r_R, eik2r_R, is_ibz2):
"""Calculate Coulomb interactions.
For all n1 in the n1_n list, calculate interaction with n2."""
# number of plane waves:
ng1 = self.wfs.ng_k[kpt1.k]
ng2 = self.wfs.ng_k[kpt2.k]
# Transform to real space and apply symmetry operation:
self.timer.start('IFFT1')
if is_ibz2:
u2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k)
else:
psit2_R = self.pd.ifft(kpt2.psit_nG[n2, :ng2], kpt2.k) * eik20r_R
self.timer.start('Symmetry transform')
u2_R = self.kd.transform_wave_function(psit2_R, k) / eik2r_R
self.timer.stop()
self.timer.stop()
# Calculate pair densities:
nt_nG = self.pd2.zeros(len(n1_n), q=q)
for n1, nt_G in zip(n1_n, nt_nG):
self.timer.start('IFFT2')
u1_R = self.pd.ifft(kpt1.psit_nG[n1, :ng1], kpt1.k)
self.timer.stop()
nt_R = u1_R.conj() * u2_R
self.timer.start('FFT')
nt_G[:] = self.pd2.fft(nt_R, q)
self.timer.stop()
s = self.kd.sym_k[k]
time_reversal = self.kd.time_reversal_k[k]
k2_c = self.kd.ibzk_kc[kpt2.k]
self.timer.start('Compensation charges')
Q_anL = {} # coefficients for shape functions
for a, P1_ni in kpt1.P_ani.items():
P1_ni = P1_ni[n1_n]
if is_ibz2:
P2_i = kpt2.P_ani[a][n2]
else:
b = self.kd.symmetry.a_sa[s, a]
S_c = (np.dot(self.spos_ac[a], self.kd.symmetry.op_scc[s]) -
self.spos_ac[b])
assert abs(S_c.round() - S_c).max() < 1e-5
if self.ghat.dtype == complex:
x = np.exp(2j * pi * np.dot(k2_c, S_c))
else:
x = 1.0
P2_i = np.dot(self.wfs.setups[a].R_sii[s],
kpt2.P_ani[b][n2]) * x
if time_reversal:
P2_i = P2_i.conj()
D_np = []
for P1_i in P1_ni:
D_ii = np.outer(P1_i.conj(), P2_i)
D_np.append(pack(D_ii))
Q_anL[a] = np.dot(D_np, self.wfs.setups[a].Delta_pL)
self.timer.start('Expand')
if q != self.qlatest:
self.f_IG = self.ghat.expand(q)
self.qlatest = q
self.timer.stop('Expand')
# Add compensation charges:
self.ghat.add(nt_nG, Q_anL, q, self.f_IG)
self.timer.stop('Compensation charges')
if self.molecule and n2 in n1_n:
nn = (n1_n == n2).nonzero()[0][0]
nt_nG[nn] -= self.ngauss_G
else:
nn = None
iG2_G = self.iG2_qG[q]
# Calculate energies:
e_n = np.empty(len(n1_n))
for n, nt_G in enumerate(nt_nG):
e_n[n] = -4 * pi * np.real(self.pd2.integrate(nt_G, nt_G * iG2_G))
self.npairs += 1
if nn is not None:
e_n[nn] -= 2 * (self.pd2.integrate(nt_nG[nn], self.vgauss_G) +
(self.beta / 2 / pi)**0.5)
if self.write_timing_information:
t = (time() - self.t0) / len(n1_n)
self.log('Time for first pair-density: %10.3f seconds' % t)
self.log('Estimated total time: %10.3f seconds' %
(t * self.npairs0 / self.world.size))
self.write_timing_information = False
return e_n
def calculate_exx_paw_correction(self):
self.timer.start('PAW correction')
self.devv = 0.0
self.evc = 0.0
self.ecc = 0.0
deg = 2 // self.wfs.nspins # spin degeneracy
for a, D_sp in self.dens.D_asp.items():
setup = self.wfs.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
self.devv -= D_ii[i1, i2] * A / deg
self.evc -= np.dot(D_p, setup.X_p)
self.ecc += setup.ExxC
if not self.bandstructure:
self.timer.stop('PAW correction')
return
Q = self.world.size // self.wfs.kd.comm.size
self.exx_skn *= Q
for kpt in self.wfs.kpt_u:
for a, D_sp in self.dens.D_asp.items():
setup = self.wfs.setups[a]
for D_p in D_sp:
D_ii = unpack2(D_p)
ni = len(D_ii)
P_ni = kpt.P_ani[a]
for i1 in range(ni):
for i2 in range(ni):
A = 0.0
for i3 in range(ni):
p13 = packed_index(i1, i3, ni)
for i4 in range(ni):
p24 = packed_index(i2, i4, ni)
A += setup.M_pp[p13, p24] * D_ii[i3, i4]
self.exx_skn[kpt.s, kpt.k] -= \
(A * P_ni[:, i1].conj() * P_ni[:, i2]).real
p12 = packed_index(i1, i2, ni)
self.exx_skn[kpt.s, kpt.k] -= \
(P_ni[:, i1].conj() * setup.X_p[p12] *
P_ni[:, i2]).real / self.wfs.nspins
self.world.sum(self.exx_skn)
self.exx_skn *= self.hybrid / Q
self.timer.stop('PAW correction')
def initialize_gaussian(self):
"""Calculate gaussian compensation charge and its potential.
Used to decouple electrostatic interactions between
periodically repeated images for molecular calculations.
Charge containing one electron::
(beta/pi)^(3/2)*exp(-beta*r^2),
its Fourier transform::
exp(-G^2/(4*beta)),
and its potential::
erf(beta^0.5*r)/r.
"""
gd = self.wfs.gd
# Set exponent of exp-function to -19 on the boundary:
self.beta = 4 * 19 * (gd.icell_cv**2).sum(1).max()
# Calculate gaussian:
G_Gv = self.pd2.G_Qv[self.pd2.Q_qG[0]]
G2_G = self.pd2.G2_qG[0]
C_v = gd.cell_cv.sum(0) / 2 # center of cell
self.ngauss_G = np.exp(-1.0 / (4 * self.beta) * G2_G +
1j * np.dot(G_Gv, C_v)) / gd.dv
# Calculate potential from gaussian:
R_Rv = gd.get_grid_point_coordinates().transpose((1, 2, 3, 0))
r_R = ((R_Rv - C_v)**2).sum(3)**0.5
if (gd.N_c % 2 == 0).all():
r_R[tuple(gd.N_c // 2)] = 1.0 # avoid dividing by zero
v_R = erf(self.beta**0.5 * r_R) / r_R
if (gd.N_c % 2 == 0).all():
v_R[tuple(gd.N_c // 2)] = (4 * self.beta / pi)**0.5
self.vgauss_G = self.pd2.fft(v_R)
# Compare self-interaction to analytic result:
assert abs(0.5 * self.pd2.integrate(self.ngauss_G, self.vgauss_G) -
(self.beta / 2 / pi)**0.5) < 1e-6
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss=self.fullkss
finegrid=self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print >> self.txt,'RPA',nij,'transitions'
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt,'RPA kss['+'%d'%ij+']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
## print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p,phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij,nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
timer2.start('integrate')
pre = 2.*sqrt(kss[ij].get_energy()*kss[kq].get_energy()*
kss[ij].get_weight()*kss[kq].get_weight())
Om[ij,kq]= pre * self.gd.integrate(rhot*phit)
## print "int=",Om[ij,kq]
timer2.stop()
# Add atomic corrections
timer2.start('integrate corrections 2')
Ia = 0.
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pkq_ni = wfs.kpt_u[kss[kq].spin].P_ani[a]
Pk_i = Pkq_ni[kss[kq].i]
Pq_i = Pkq_ni[kss[kq].j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0*np.dot(Dkq_p,np.dot(C_pp,Dij_p))
timer2.stop()
Om[ij,kq] += pre * self.gd.comm.sum(Ia)
if ij == kq:
Om[ij,kq] += kss[ij].get_energy()**2
else:
Om[kq,ij]=Om[ij,kq]
timer.stop()
## timer2.write()
if ij < (nij-1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5*t*(nij-ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPA estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
def get_rpa(self):
"""Calculate RPA and Hartree-fock part of the A+-B matrices."""
# shorthands
kss = self.fullkss
finegrid = self.finegrid
# calculate omega matrix
nij = len(kss)
print >> self.txt, 'RPAhyb', nij, 'transitions'
AmB = np.zeros((nij, nij))
ApB = self.ApB
# storage place for Coulomb integrals
integrals = {}
for ij in range(nij):
print >> self.txt,'RPAhyb kss['+'%d'%ij+']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(
finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype)
self.poisson.solve(phit_p,rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
self.restrict(phit_p, phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij, nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(
finegrid is 2)
timer2.stop()
pre = self.weight_Kijkq(ij, kq)
timer2.start('integrate')
I = self.Coulomb_integral_kss(kss[ij], kss[kq], phit, rhot)
if kss[ij].spin == kss[kq].spin:
name = self.Coulomb_integral_name(kss[ij].i, kss[ij].j,
kss[kq].i, kss[kq].j,
kss[ij].spin )
integrals[name] = I
ApB[ij,kq]= pre * I
timer2.stop()
if ij == kq:
epsij = kss[ij].get_energy() / kss[ij].get_weight()
AmB[ij,kq] += epsij
ApB[ij,kq] += epsij
timer.stop()
## timer2.write()
if ij < (nij - 1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5*t*(nij-ij) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPAhyb estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
# add HF parts and apply symmetry
timer.start('RPA hyb HF part')
if hasattr(self.xc, 'hybrid'):
weight = self.xc.hybrid
else:
weight = 0.0
for ij in range(nij):
i = kss[ij].i
j = kss[ij].j
s = kss[ij].spin
for kq in range(ij,nij):
if kss[ij].pspin == kss[kq].pspin:
k = kss[kq].i
q = kss[kq].j
ikjq = self.Coulomb_integral_ijkq(i, k, j, q, s, integrals)
iqkj = self.Coulomb_integral_ijkq(i, q, k, j, s, integrals)
ApB[ij,kq] -= weight * ( ikjq + iqkj )
AmB[ij,kq] -= weight * ( ikjq - iqkj )
ApB[kq,ij] = ApB[ij,kq]
AmB[kq,ij] = AmB[ij,kq]
timer.stop()
return AmB
def get_rpa(self):
"""calculate RPA part of the omega matrix"""
# shorthands
kss = self.fullkss
finegrid = self.finegrid
wfs = self.paw.wfs
eh_comm = self.eh_comm
# calculate omega matrix
nij = len(kss)
print >> self.txt, 'RPA', nij, 'transitions'
Om = self.Om
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt, 'RPA kss[' + '%d' % ij + ']=', kss[ij]
timer = Timer()
timer.start('init')
timer2 = Timer()
# smooth density including compensation charges
timer2.start('with_compensation_charges 0')
rhot_p = kss[ij].with_compensation_charges(finegrid is not 0)
timer2.stop()
# integrate with 1/|r_1-r_2|
timer2.start('poisson')
phit_p = np.zeros(rhot_p.shape, rhot_p.dtype.char)
self.poisson.solve(phit_p, rhot_p, charge=None)
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
if finegrid == 1:
rhot = kss[ij].with_compensation_charges()
phit = self.gd.zeros()
## print "shapes 0=",phit.shape,rhot.shape
self.restrict(phit_p, phit)
else:
phit = phit_p
rhot = rhot_p
for kq in range(ij, nij):
if kq != ij:
# smooth density including compensation charges
timer2.start('kq with_compensation_charges')
rhot = kss[kq].with_compensation_charges(finegrid is 2)
timer2.stop()
timer2.start('integrate')
pre = 2. * sqrt(kss[ij].get_energy() * kss[kq].get_energy() *
kss[ij].get_weight() * kss[kq].get_weight())
Om[ij, kq] = pre * self.gd.integrate(rhot * phit)
## print "int=",Om[ij,kq]
timer2.stop()
# Add atomic corrections
timer2.start('integrate corrections 2')
Ia = 0.
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
Dij_ii = np.outer(Pi_i, Pj_i)
Dij_p = pack(Dij_ii)
Pkq_ni = wfs.kpt_u[kss[kq].spin].P_ani[a]
Pk_i = Pkq_ni[kss[kq].i]
Pq_i = Pkq_ni[kss[kq].j]
Dkq_ii = np.outer(Pk_i, Pq_i)
Dkq_p = pack(Dkq_ii)
C_pp = wfs.setups[a].M_pp
# ----
# 2 > P P C P P
# ---- ip jr prst ks qt
# prst
Ia += 2.0 * np.dot(Dkq_p, np.dot(C_pp, Dij_p))
timer2.stop()
Om[ij, kq] += pre * self.gd.comm.sum(Ia)
if ij == kq:
Om[ij, kq] += kss[ij].get_energy()**2
else:
Om[kq, ij] = Om[ij, kq]
timer.stop()
## timer2.write()
if ij < (nij - 1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij
) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'RPA estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
def get_xc(self):
"""Add xc part of the coupling matrix"""
# shorthands
paw = self.paw
wfs = paw.wfs
gd = paw.density.finegd
comm = gd.comm
eh_comm = self.eh_comm
fg = self.finegrid is 2
kss = self.fullkss
nij = len(kss)
Om_xc = self.Om
# initialize densities
# nt_sg is the smooth density on the fine grid with spin index
if kss.nvspins == 2:
# spin polarised ground state calc.
nt_sg = paw.density.nt_sg
else:
# spin unpolarised ground state calc.
if kss.npspins == 2:
# construct spin polarised densities
nt_sg = np.array(
[.5 * paw.density.nt_sg[0], .5 * paw.density.nt_sg[0]])
else:
nt_sg = paw.density.nt_sg
# check if D_sp have been changed before
D_asp = self.paw.density.D_asp
for a, D_sp in D_asp.items():
if len(D_sp) != kss.npspins:
if len(D_sp) == 1:
D_asp[a] = np.array([0.5 * D_sp[0], 0.5 * D_sp[0]])
else:
D_asp[a] = np.array([D_sp[0] + D_sp[1]])
# restrict the density if needed
if fg:
nt_s = nt_sg
else:
nt_s = self.gd.zeros(nt_sg.shape[0])
for s in range(nt_sg.shape[0]):
self.restrict(nt_sg[s], nt_s[s])
gd = paw.density.gd
# initialize vxc or fxc
if self.derivativeLevel == 0:
raise NotImplementedError
if kss.npspins == 2:
v_g = nt_sg[0].copy()
else:
v_g = nt_sg.copy()
elif self.derivativeLevel == 1:
pass
elif self.derivativeLevel == 2:
raise NotImplementedError
if kss.npspins == 2:
fxc = d2Excdnsdnt(nt_sg[0], nt_sg[1])
else:
fxc = d2Excdn2(nt_sg)
else:
raise ValueError('derivativeLevel can only be 0,1,2')
## self.paw.my_nuclei = []
ns = self.numscale
xc = self.xc
print >> self.txt, 'XC', nij, 'transitions'
for ij in range(eh_comm.rank, nij, eh_comm.size):
print >> self.txt, 'XC kss[' + '%d' % ij + ']'
timer = Timer()
timer.start('init')
timer2 = Timer()
if self.derivativeLevel == 1:
# vxc is available
# We use the numerical two point formula for calculating
# the integral over fxc*n_ij. The results are
# vvt_s smooth integral
# nucleus.I_sp atom based correction matrices (pack2)
# stored on each nucleus
timer2.start('init v grids')
vp_s = np.zeros(nt_s.shape, nt_s.dtype.char)
vm_s = np.zeros(nt_s.shape, nt_s.dtype.char)
if kss.npspins == 2: # spin polarised
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] += ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vp_s)
nv_s = nt_s.copy()
nv_s[kss[ij].pspin] -= ns * kss[ij].get(fg)
xc.calculate(gd, nv_s, vm_s)
else: # spin unpolarised
nv = nt_s + ns * kss[ij].get(fg)
xc.calculate(gd, nv, vp_s)
nv = nt_s - ns * kss[ij].get(fg)
xc.calculate(gd, nv, vm_s)
vvt_s = (0.5 / ns) * (vp_s - vm_s)
timer2.stop()
# initialize the correction matrices
timer2.start('init v corrections')
I_asp = {}
for a, P_ni in wfs.kpt_u[kss[ij].spin].P_ani.items():
# create the modified density matrix
Pi_i = P_ni[kss[ij].i]
Pj_i = P_ni[kss[ij].j]
P_ii = np.outer(Pi_i, Pj_i)
# we need the symmetric form, hence we can pack
P_p = pack(P_ii)
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] -= ns * P_p
setup = wfs.setups[a]
I_sp = np.zeros_like(D_sp)
setup.xc_correction.calculate(self.xc, D_sp, I_sp)
I_sp *= -1.0
D_sp = self.paw.density.D_asp[a].copy()
D_sp[kss[ij].pspin] += ns * P_p
setup.xc_correction.calculate(self.xc, D_sp, I_sp)
I_sp /= 2.0 * ns
I_asp[a] = I_sp
timer2.stop()
timer.stop()
t0 = timer.get_time('init')
timer.start(ij)
for kq in range(ij, nij):
weight = self.weight_Kijkq(ij, kq)
if self.derivativeLevel == 0:
# only Exc is available
if kss.npspins == 2: # spin polarised
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] +=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] +=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] -= \
kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -=\
kss[ij].get(fg)
nv_g[kss[kq].pspin] +=\
kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
nv_g = nt_sg.copy()
nv_g[kss[ij].pspin] -= \
kss[ij].get(fg)
nv_g[kss[kq].pspin] -=\
kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(\
nv_g[0],v_g,nv_g[1],v_g)
else: # spin unpolarised
nv_g=nt_sg + ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excpp = xc.get_energy_and_potential(nv_g, v_g)
nv_g=nt_sg + ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excpm = xc.get_energy_and_potential(nv_g, v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
+ ns*kss[kq].get(fg)
Excmp = xc.get_energy_and_potential(nv_g, v_g)
nv_g=nt_sg - ns*kss[ij].get(fg)\
- ns*kss[kq].get(fg)
Excmm = xc.get_energy_and_potential(nv_g, v_g)
Om_xc[ij,kq] += weight *\
0.25*(Excpp-Excmp-Excpm+Excmm)/(ns*ns)
elif self.derivativeLevel == 1:
# vxc is available
timer2.start('integrate')
Om_xc[ij,kq] += weight*\
self.gd.integrate(kss[kq].get(fg)*
vvt_s[kss[kq].pspin])
timer2.stop()
timer2.start('integrate corrections')
Exc = 0.
for a, P_ni in wfs.kpt_u[kss[kq].spin].P_ani.items():
# create the modified density matrix
Pk_i = P_ni[kss[kq].i]
Pq_i = P_ni[kss[kq].j]
P_ii = np.outer(Pk_i, Pq_i)
# we need the symmetric form, hence we can pack
# use pack as I_sp used pack2
P_p = pack(P_ii)
Exc += np.dot(I_asp[a][kss[kq].pspin], P_p)
Om_xc[ij, kq] += weight * self.gd.comm.sum(Exc)
timer2.stop()
elif self.derivativeLevel == 2:
# fxc is available
if kss.npspins == 2: # spin polarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg)*
kss[kq].get(fg)*
fxc[kss[ij].pspin,kss[kq].pspin])
else: # spin unpolarised
Om_xc[ij,kq] += weight *\
gd.integrate(kss[ij].get(fg)*
kss[kq].get(fg)*
fxc)
if ij != kq:
Om_xc[kq, ij] = Om_xc[ij, kq]
timer.stop()
## timer2.write()
if ij < (nij - 1):
t = timer.get_time(ij) # time for nij-ij calculations
t = .5 * t * (nij - ij
) # estimated time for n*(n+1)/2, n=nij-(ij+1)
print >> self.txt,'XC estimated time left',\
self.timestring(t0*(nij-ij-1)+t)
class DipoleQuad:
""" Class to handle external potential due to
dipole and quadrupole from SCME type
calculator object.
"""
def __init__(self, mm, qm, mp, calcmm, dyn=False, g=0.5):
self.mm = mm # mm atoms object
self.mp = mp # no. atoms per center of mass (cm)
self.dyn = dyn # dyn. update of potential?
self.calcmm = calcmm # mm calculator (SCME)
self.qm = qm # qm atoms object
#
self.qmidx = len(qm)# no. QM atoms
#
self.nm = len(self.mm) / self.mp
self.cm = self.get_cm(self.nm)
self.timer = Timer()
# smoothing value
self.g = g
# initialization
self.initial = True
# Hold on to old arrays
self.dipoles = None
self.qpoles = None
self.dipoles_1 = None
self.qpoles_1 = None
def get_potential(self, gd=None, density=None,
setups=None, nspins=None):
""" Create external potential from dipoles
and quadrupoles with origin at the
center of mass of each classical
molecule in the atoms object """
if self.initial:
self.update_potential(gd=gd, density=density,
setups=setups, nspins=nspins)
return self.potential
elif self.dyn:
if not self.check_convergence():
self.update_potential(gd=gd, density=density,
setups=setups, nspins=nspins)
return self.potential
else:
if hasattr(self, 'potential'):
if gd == self.gd or gd is None:
# Nothing changed
return self.potential
def update_potential(self, gd=None, density=None,
setups=None, nspins=None):
# Save old dipoles
if self.dipoles is not None:
self.dipoles_1 = self.dipoles.copy()
self.qpoles_1 = self.qpoles.copy()
self.gd = gd
# Grab electric field and derivative values
self.timer.start('Electric Field and Derivative')
eF, deF = self.get_efield(density, setups, nspins)
self.timer.stop('Electric Field and Derivative')
calcmm = self.calcmm
mm = self.mm
#######################################
# Pass (new) values to SCME
calcmm.eF = eF # <-- ! CHECK
calcmm.deF = deF
self.timer.start('SCME Calculation')
calcmm.calculate(mm)
self.timer.stop('SCME Calculation')
#######################################
# Values are in atomic-units
dipole = calcmm.dipoles / Bohr
qpoles = calcmm.qpoles / Bohr**2
#
if rank == MASTER:
print 'dipoles'
print dipole * Bohr / Debye
print 'qpoles'
print qpoles * Bohr**2 / Debye
# No. solvent mols
n = len(self.mm) / self.mp
# Make empty POT
potential = np.zeros(gd.end_c-gd.beg_c)
sG = (np.indices(gd.n_c, float).T + \
gd.beg_c) / gd.N_c
# Dipole is something with Bohr**2
# Place external potential due to Dipoles and Quads on grid
# For a given MM mol, get all distances
for a in range(n):
nsG = sG - np.linalg.solve(gd.cell_cv.T, self.cm[a])
# drX, drY, drZ distances:
xyz = np.dot(nsG, gd.cell_cv)
# mUr
mUr = np.dot(xyz,dipole[a])
#
Q = qpoles[a,:,:]
# |r - rcm|
dis = np.sqrt(((xyz.T)**2).sum(axis=0))
dis_d = smooth(dis, self.g)
dis_q = smooth(dis, 0.3)
# Add dipole component
potential += mUr.T / dis_d**3
# Quadrupole components:
for i in range(3):
for j in range(3):
potential += Q[i,j]*xyz.T[i,:,:,:]*xyz.T[j,:,:,:] / dis_q**5
if i == j:
potential -= 1./3 * Q[i,j] / dis_q**3
# Potential updated
self.initial = False
# Hold on to
self.gd = gd
self.potential = potential
self.eF = eF
self.deF = deF
self.qpoles = qpoles.copy()
self.dipoles = dipole.copy()
def check_convergence(self):
if self.dipoles_1 is not None:
dip = abs(self.dipoles - self.dipoles_1).sum()
qua = abs(self.qpoles - self.qpoles_1).sum()
if rank == MASTER:
print dip, qua
return np.max([dip]) < 1e-5
else:
return False
def get_efield(self, density, setups, nspins):
""" Evaluate electric field at each cm
from total psuedo charge density.
"""
gd = self.gd
eF = np.zeros((3,self.nm))
deF = np.zeros((3,3,self.nm))
# Grab comp. charges
comp = np.zeros(self.qmidx)
density.Q_aL = {}
for a, D_sp in density.D_asp.items():
Q_L = density.Q_aL[a] = np.dot(D_sp[:nspins].sum(0),
setups[a].Delta_pL)
Q_L[0] += setups[a].Delta0
comp[a] += Q_L[0]
# Collect over gd domains
#wfs.gd.comm.sum(comp)
comp *= -1*sqrt(4.*pi)
# Grab pseudo-density on gd
if density.nt_sg is None:
density.interpolate_pseudo_density()
nt_sG = density.nt_sg
#
if density.nspins == 1:
nt_g = nt_sG[0]
else:
nt_g = nt_sG.sum(axis=0)
#assert np.shape(nt_g) == np.shape(self.gd)
#
sG = (np.indices(gd.n_c, float).T + \
gd.beg_c) / gd.N_c
# Arrays
#
for a, pos in enumerate(self.cm):
# Get all gpt distances relative to molecule a
nsG = sG - np.linalg.solve(gd.cell_cv.T, self.cm[a])
# r(xyz) to all gpts
xyz = np.dot(nsG, gd.cell_cv)
# distance to all gpts
dis = np.sqrt(((xyz.T)**2).sum(axis=0))
# dis = smooth(dis, self.g)
# total field on cm due to density
eFT = (xyz.T)*nt_g*gd.dv / dis**3
eF[:,a] += [eFT[0].sum(),eFT[1].sum(),eFT[2].sum()]
# nuclei-to-dipole
xyz_n = self.qm.get_positions() / Bohr - pos
dis_n = np.sqrt((xyz_n**2).sum(axis=1))
eF[:,a] -= (xyz_n.T * comp / dis_n**3).T.sum(axis=0)
# Loop for deF
for n in range(3):
# ...
nr_ir = xyz.T[n]*xyz.T*nt_g*3.*gd.dv / dis**5
deF[n,:,a] -= [nr_ir[0].sum(),nr_ir[1].sum(),nr_ir[2].sum()]
deF[n,n,a] += (nt_g*gd.dv / dis**3).sum()
# comp
deF[n,:,a] += 3*(xyz_n.T[n]*xyz_n.T*comp / dis_n**5).T.sum(axis=0)
deF[n,n,a] -= (comp / dis_n**3).sum()
gd.comm.sum(eF)
gd.comm.sum(deF)
# Change units to D/A, D/AA
return eF/Bohr**2, deF/Bohr**3
def get_nuclear_energy(self, nucleus):
return -1. * nucleus.setup.Z * self.get_value(spos_c = nucleus.spos_c)
def get_value(self, position=None, spos_c=None):
""" Potential value as seen by an electron at a
certain gridpoint """
if position is None:
vr = spos_c * self.gd.h_cv * self.gd.N_c
else:
vr = position
dipole = self.dipole
quad = self.quad
n = len(self.atoms / self.mp)
self.get_cm(n,self.mp)
v = 0
# Eval. external potential at vr
for a in range(n):
dr = vr - self.cm[a]
dis = np.sqrt((dr**2).sum())
# mUr
mUr = np.dot(dis,dipole[a])
Q = quad[:,:,a]
v += mUr / dis**3
return v
def get_taylor(self, position=None, spos_c=None):
return [[0]]
def get_cm(self, n):
cm = np.zeros((n,3))
atoms = self.mm
mp = self.mp
for i in range(n):
cm[i,:] += atoms[i*mp:(i+1)*mp].get_center_of_mass() / Bohr
return cm